I don't have 2-3 dogs but I do have one and have had the same concerns in not wanting them to play in the same area as the dog goes to the bathroom. What has worked for me is I just have him on a leash attached to the porch so that he can only go in the specific area. The kids that I watch kind of know the routine whenever we go in the yard and that is that they wait for me to do a quick search and poop pick up before they can play. Because it's winter I still do the same thing but then I throw tons of fresh snow on top so they aren't tromping through it as well. It's funny because if they do find something that I have missed they all stop and start yelling and pointing 'Miss D! There's Poop!!!!' that and yesterday as I was trying to pick up before the kids arrived my son was with me and started yelling 'I got it! I got it!' and ran up to me with his shovel with a scoop of poop in it. LOL!!

As for a run (I thought of that too but because of the layout of my house it won't work). I would suggest to not have a flooring because chances are they won't go to the bathroom on it. Maybe just get a chain link fence of some sort - I've seen lots of people selling them on Kijiji

BTW 3 dogs and a day home!? How do you do it? You're my hero! Lol!

Hope that helped